Variability is a near-ubiquitous characteristic of the young, low-mass, accreting stars known as Classical T Tauri Stars (CTTS). The driving forces behind minute-timescale accretion variability remain poorly understood and can only be probed with multi-wavelength, simultaneous observations. Here, we present simultaneous, short-cadence light curves from the Transiting Exoplanet Survey Satellite (TESS) and ground-based UBVRI photometry from the Lowell Discovery Telescope (LDT) for 14 well-studied CTTS in the Taurus star-forming region (~2 Myr). We derived empirical variability classifications for each object and measured correlations between the observed flux in the TESS bandpass and accretion. We identified quasi-periodic fluctuations on timescales of minutes, which may be evidence of thermal instabilities at the base of the accretion column near the surface of the star. For one of these targets, GM Aur, we present six epochs of near-ultraviolet to optical, medium resolution spectra from the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) that were obtained simultaneously with the TESS observations. Using accretion shock models, we decomposed the observed spectra into a distribution of accretion column densities and found that the TESS bandpass tends to trace changes in the low-density regions of the accretion flow. In addition to aiding in the interpretation of future TESS light curves of CTTS, this unique dataset will serve as a test for the upcoming Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) HST program, which has devoted 500 orbits to studying the ultraviolet emission of young, low-mass stars.